Basic properties
| Modulus: | \(3724\) | |
| Conductor: | \(931\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(126\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{931}(272,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3724.eq
\(\chi_{3724}(237,\cdot)\) \(\chi_{3724}(321,\cdot)\) \(\chi_{3724}(377,\cdot)\) \(\chi_{3724}(405,\cdot)\) \(\chi_{3724}(461,\cdot)\) \(\chi_{3724}(517,\cdot)\) \(\chi_{3724}(769,\cdot)\) \(\chi_{3724}(853,\cdot)\) \(\chi_{3724}(909,\cdot)\) \(\chi_{3724}(937,\cdot)\) \(\chi_{3724}(993,\cdot)\) \(\chi_{3724}(1049,\cdot)\) \(\chi_{3724}(1301,\cdot)\) \(\chi_{3724}(1385,\cdot)\) \(\chi_{3724}(1441,\cdot)\) \(\chi_{3724}(1525,\cdot)\) \(\chi_{3724}(1581,\cdot)\) \(\chi_{3724}(1833,\cdot)\) \(\chi_{3724}(1917,\cdot)\) \(\chi_{3724}(1973,\cdot)\) \(\chi_{3724}(2001,\cdot)\) \(\chi_{3724}(2113,\cdot)\) \(\chi_{3724}(2365,\cdot)\) \(\chi_{3724}(2505,\cdot)\) \(\chi_{3724}(2533,\cdot)\) \(\chi_{3724}(2589,\cdot)\) \(\chi_{3724}(2897,\cdot)\) \(\chi_{3724}(2981,\cdot)\) \(\chi_{3724}(3065,\cdot)\) \(\chi_{3724}(3121,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((1863,3041,3137)\) → \((1,e\left(\frac{1}{14}\right),e\left(\frac{7}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 3724 }(3065, a) \) | \(-1\) | \(1\) | \(e\left(\frac{23}{126}\right)\) | \(e\left(\frac{65}{126}\right)\) | \(e\left(\frac{23}{63}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{31}{126}\right)\) | \(e\left(\frac{44}{63}\right)\) | \(e\left(\frac{71}{126}\right)\) | \(e\left(\frac{17}{63}\right)\) | \(e\left(\frac{2}{63}\right)\) | \(e\left(\frac{23}{42}\right)\) |